How can entropy both decrease predictability and promote even distributions?

There is no uniformity, and the level of prediction is high. You immediately see that the person on the left is rich, the one on the right is poor. You know who'll have a good meal tonight. Who has higher life expectancy. And so on.

Consider this now:

High uniformity, low prediction. Prison uniforms, well, they uniformize. From the picture, you can't get much information, apart from the fact that they are in prison.

Therefore: the first picture carries a lot of information about the people. The second doesn't. High entropy for the first, low for the second.

An unequal distribution of income produces the first picture. A uniform distribution produces the second one.

Interesting, this is what happens to societies, organizations, and organisms. They start with low entropy (uniformity, equality) and develop towards higher complexity (i.e. specialization, inequality).